Thanks for clearing the confusion. So what I have used is basically an MDP. But what factors make a diffusion approach different from that of an MDP? Is it the reduction by a geometric progression in case of diffusion and an arithmetic reduction in terms of a simple MDP? Or is it some different factor? Right now, they both seem very similar to me. Sorry for all the annoying questions, but I was probably a bit too lazy to search it in Google!

Not sure if I have understood it correctly, but seems like a repulsive scent would prevent the ant from moving towards the enemy and take a longer path to the food in your example, which might be a better choice. I was taking the Stanford online class and can recollect a policy function which would consider a bad guy between an agent and a goal state. So looks like the repulsive scent in the diffusion value is a good approximation of such a policy function...

But again, the enemy seems closer to the food than my ant. This case might need to be evaluated differently based on different scenarios. If it is a 2 player game (which might be difficult to detect in the first place) then I guess attacking the enemy would be a better choice than trying to find a path to the food around the enemy. A greedy heuristic (without prediction of future moves) of denying food to the enemy and preferring a 1 v 1 exchange might look like a better strategy at first. However, it might be a bad idea after all, especially considering that the top bots often prefer to avoid 1 v 1 exchanges!

As far as I remember, in Stanford AI class, the bad guy and the goal were in an exercise asking how to look for good feature choice. Not in a policy function. Because value-iteration-based planning on deterministic maps always consider only the best neighbor.

And, for your second paragraph, I chose wrong example. Let's replace the food by a B hill, and it will be fine !

Thanks again for the explanations. The long wait is now finally over. Just read the post that GreenTea was placed above xathis in the last 2 hours. However xathis still wins (and deserved to win for dominating the server for 2 months)!